Question

A marble is randomly selected from a bag. The probability of selecting a marble with dots on it is 0.2. The probability of selecting a marble that is both purple and has dots on it is 0.1. What is the probability of selecting a purple marble given that the marble has dots on it? Enter your answer as a decimal in the box.

Answer 1

Answer:

0.5

Step-by-step explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots, $P(D \cap P)=0.1$

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

$P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5$

The probability of selecting a purple marble given that the marble has dots on it is 0.5.